The number of problem families "turned around" by a government scheme has almost doubled in the last six months.

David Cameron set out an ambitious plan to help 120,000 "troubled" households by May 2015 as part of his response to rioting in London and other cities, including Bristol and Gloucester, in the summer of 2013.

Blaming the disorder on broken homes, he offered English councils financial incentives to get truanting children back to school, adults into work and antisocial behaviour arrested – backed by a budget of over £400 million.

Bristol reports that it has helped over 75 per cent of its targeted families.

Public spending watchdogs warned in recent weeks that the initiative risked falling short of expectations, with MPs pointing the finger at a "baffling" failure of Whitehall co-ordination for delays.

The Commons public accounts committee called for further improvements in data-sharing, action to tackle wide variations in the performance of councils and firms delivering the help, and an increase in the pace of progress.

But the Prime Minister hailed the latest figures supplied by councils – some of which said they have dealt with three-quarters of the families in their areas – as evidence that people were being assisted and that the taxpayer was saving money.

The Department for Communities and Local Government (DCLG) said the 39,480 families where children had now been to school for three consecutive terms, youth crime and antisocial behaviour significantly reduced and adults found work for at least three months would otherwise have cost the state £3billion a year.

So far, 111,000 have been identified for help, with 97,000 being actively worked on, DCLG said.